Mathematical models of a liquid filtration from reservoirs

Anvarbek Meirmanov, Nelly Erygina, Saltanbek Mukhambetzhanov
Abstract:
This article studies the filtration from reservoirs into porous
media under gravity. We start with the exact mathematical model at
the microscopic level, describing the joint motion of a liquid in reservoir
and the same liquid and the elastic solid skeleton in the porous medium.
Then using a homogenization procedure we derive the chain of macroscopic
models from the poroelasticity equations up to the simplest Darcy's law
in the porous medium and hydraulics in the reservoir.